Visualizing the Reciprocal

[kouranjelika]

Hi Guys,

So we just did Thursday with Ron on Creative Problem Solving (rather Flexible).

And there was word problem that was this in a nutshell:
n<0
n^2 > 1/100
What range must the reciprocal of n be in?

I originally approached it as follows:
Since n^2 < 1/100: |n|<1/10
then we know n<0; so -n<1/10: n>-1/10, which works I guess. The range of n is between -1/10 and 0. What threw me for some reason in this case was the reciprocal. I was trying to visualize it on the number line and realize I didn't know how. Is that possible to do?

Thanks,
Anjelika

[jnelson0612]

Hi Guys,

So we just did Thursday with Ron on Creative Problem Solving (rather Flexible).

And there was word problem that was this in a nutshell:
n<0
n^2 > 1/100
What range must the reciprocal of n be in?

I originally approached it as follows:
Since n^2 < 1/100: |n|<1/10
then we know n<0; so -n<1/10: n>-1/10, which works I guess. The range of n is between -1/10 and 0. What threw me for some reason in this case was the reciprocal. I was trying to visualize it on the number line and realize I didn't know how. Is that possible to do?

Thanks,
Anjelika

Anjelika,
This is a tricky problem. Let's try to make some headway with the range before we work on the reciprocal.

I'd like you to draw out a number line and plot the points 0 and -1/10. Like you said, we know that (-1/10) squared is 1/100, so that's a good boundary. Then I'd like you to choose a fraction greater than -1/10 but less than zero, and then choose a number less than -1/10. Square both of them and then look at the question again. Let's refine the range before we move any further. Good luck!